/sci/ - Science & Math

Likewise, a very elegant argument can be made supporting the assumption <span class="math">y' = y[/spoiler].

Suppose that <span class="math">y'[/spoiler] is moving relative to <span class="math">y[/spoiler] as in the picture (fig. 1).

Looking at it from the other side of the paper, we see fig. 2. By the principle of relativity, fig. 2 is equivalent to fig. 3 (only relative speed matters). Therefore, fig. 3 is equivalent to fig. 1. But fig. 3 is just fig. 1 with y' and y interchanged. This can only be true in general if y' = y.